Sensitivity analysis for direct and indirect effects in the presence of exposure-induced mediator-outcome confounders

Questions of mediation are often of interest in reasoning about mechanisms, and methods have been developed to address these questions. However, these methods make strong assumptions about the absence of confounding. Even if exposure is randomized, there may be mediator-outcome confounding variables. Inference about direct and indirect effects is particularly challenging if these mediator-outcome confounders are affected by the exposure because in this case these effects are not identified irrespective of whether data is available on these exposure-induced mediator-outcome confounders. In this paper, we provide a sensitivity analysis technique for natural direct and indirect effects that is applicable even if there are mediator-outcome confounders affected by the exposure. We give techniques for both the difference and risk ratio scales and compare the technique to other possible approaches.